## What is Mass Transfer?

Mass transfer means the transport or movement of mass using streams, phases, components, and so on from one location to another.

## Convective mass transfer in chemical engineering

Mass transfer is an important phenomenon in the field of chemical engineering. The mass transfer takes place in many chemical engineering processes such as distillation, absorption, adsorption, drying, evaporation, and so on. The mass transport phenomena have a wide range of applications in various disciplines of science including chemistry, physics, chemical engineering, and pharmaceutical branches. The concept of convective mass transfer is most widely used by chemical engineers. The convective mass transfer is the concept related to the liquid and gaseous phases of a substance. In the convective mass transfer, the transport of material takes place between two surfaces of different phases, such as between a solid and a liquid surface, or between two immiscible liquids. In the case of mass transfer between two phases, a concentration gradient is formed in each phase, which allows the mass transfer to occur. Following are the cases of convective mass transfer:

- The mass transport phenomena take place only in a single phase, to or from the phase boundary.
- The mass transport phenomena take place in two contact phases.

## Convective mass transfer coefficient

The convective mass transfer coefficient is another important parameter in the field of chemical engineering and needs to be studied thoroughly by chemical engineers. In general, the mass transfer coefficient of any phase of a substance is given by the following equation,

${k}_{c}=\frac{{N}_{A}}{\u2206{C}_{A}}$

Where

- ${k}_{c}$ is the Mass transfer coefficient
- ${N}_{A}$ is the molar flux
- $\u2206{C}_{A}$ is the concentration driving force.

In the case of convective heat transfer, the heat transfer coefficient is given as,

$q=h.(T-{T}_{f})$

Where

- $h$ is the heat transfer coefficient,
- $T$ is the surface temperature of the object
- ${T}_{f}$ is the temperature of the fluid
- $q$ is the heat transferred per unit time per area of an object.

Hence,

$q$ is given as,

$q=Q/A$

Where

- $Q$ is the heat transferred per unit time
- $A$ is the area of the object.

## Parameters in convective mass transfer

The parameters in convective mass transfer are one of the most important parameters and need to be studied thoroughly by chemical engineers. The following parameters are involved in the convective mass transfer:

- Momentum diffusivity
- Thermal diffusivity
- Mass diffusivity
- Molecular diffusion
- Prandtl number
- Schmidt number
- Lewis number

### Momentum diffusivity

Momentum diffusivity is most commonly related to the fluid phase of the particle. Due to momentum diffusivity, the momentum is distributed among the flowing particles due to the effect of pressure or shear stress.

### Thermal diffusivity

Thermal diffusivity is the measurement of the rate of heat transfer of material from the hot end to the cold end.

### Mass diffusivity

Mass diffusivity is the proportionality constant between molecular flux that occurs due to the molecular diffusion and concentration gradient.

### Molecular diffusion

Molecular diffusion is the term most specifically used for the liquid and gaseous phases of a substance. Molecular diffusion is defined as the thermal motion of all the particles. Molecular diffusion is used to define the total flux of all the molecules moving from higher concentration to lower concentration zone.

### Prandtl number

Prandtl number is a dimensionless number and is defined as the ratio of momentum diffusivity and thermal diffusivity. The value of the Prandtl number very less than 1 (Prandtl number << 1) indicates that for a given substance, thermal diffusivity is dominant over the momentum diffusivity, whereas the value of Prandtl number much greater than 1 (Prandtl number >> 1) indicates that for a given substance, momentum diffusivity is dominant over the momentum diffusivity.

### Schmidt number

Schmidt number is a dimensionless number and is defined as the ratio of momentum diffusivity and mass diffusivity. The Schmidt number is used for characterizing the fluid flow and it relates to the relative thickness of the hydrodynamic layer and mass-transfer boundary layer.

### Lewis number

Lewis number is also a dimensionless number and is defined as the ratio of thermal diffusivity to mass diffusivity. The Lewis number can also be defined as the ratio of Schmidt number to Prandtl number.

## Fick's first law

Fick's First Law is an important topic in the field of chemical engineering and is studied by chemical engineers thoroughly. Fick's first law is used to control the mass transfer in a system. As per this law, the flux of diffusion from a higher concentration to a lower concentration is proportional to the concentration gradient of a substance as well as to the diffusivity of the substance in the medium. The various driving forces that contribute to the mass transfer are pressure gradient, external force, temperature gradient, chemical potential difference, and so on.

## Natural convection

Natural convection is also a term related to the liquid and gaseous phases of a substance and is an important topic in the field of chemical engineering. In natural convection, the convection does not take place due to any external effect, but convection takes place because of the properties of the substance itself. Natural convection usually occurs due to the variation in the density of molecules of the same substance. The density difference can occur due to the large variations in temperature or concentration in the substance.

## Convective mass transfer between phases

Considering a case of two immiscible or heterogeneous fluids being in contact with each other, designated as fluid A and fluid B. Considering a random substance X, which is dissolvable in fluid A as well as fluid B. When substance X is added to fluid A, substance X will start dissolving in fluid A, and as soon as fluid A and fluid B are brought together, substance X will start diffusing in fluid B as well from fluid A until the whole system reaches a specific equilibrium, provided that the two liquids, liquid A and liquid B remain in contact with each other.

## Context and Applications

The convective mass transfer between phases is used mostly by chemical engineers on regular basis. The phenomenon of diffusivity is observed when the perfume is sprayed when the smell of perfume diffuses in the air, the carbon dioxide gets diffused into the coke when the coke bottle is opened, the tea gets diffused in the water when the teabag is dipped in the water, and so on. The convective mass transfer between phases is useful for the students undergoing the following graduate courses:

- Bachelors in Engineering or Technology (Chemical)
- Masters in Technology (Chemical, Petroleum, Oil)

## Practice Problems

1. In which of the following processes mass transfer does not take place?

- Distillation
- Drying
- Heat procurement
- Evaporation

Answer: Option c

Explanation: Heat procurement is the process in which mass transfer does not take place. Distillation is the process of purifying a liquid, drying is the process of removing water from the solution, and evaporation is the process of conversion of liquid into gas.

2. The concept of convective mass transfer related to which of the following phase of a substance?

- Plasma phase
- Bose-Einstein condensate phase
- Solid-phase
- Liquid phase

Answer: Option d

Explanation: The concept of convective mass transfer is related to the liquid phase of a substance. It is not applicable for the plasma phase, Bose-Einstein condensate phase, and solid phase of a substance.

3. Which of the following is one of the parameters in convective mass transfer?

- Momentum diffusivity
- Content sorting
- Radiation
- Distillation

Answer: Option a

Explanation: Momentum diffusivity is one of the parameters involved in convective mass transfer. Content sorting, radiation, and distillation are not the parameters in convective mass transfer.

4. Which of the following is defined as the ratio of momentum diffusivity and thermal diffusivity?

- Lewis number
- Schmidt number
- Prandtl number
- Avagadro's number

Answer: Option c

Explanation: Prandtl number is defined as the ratio of momentum diffusivity and thermal diffusivity. Schmidt number is defined as the ratio of momentum diffusivity and mass diffusivity. Prandtl number is defined as the ratio of momentum diffusivity and thermal diffusivity. Avagadro's number represents the number of atoms or molecules in one mole of a substance

5. Which of the following is not one of the driving forces that contribute to the mass transfer?

- Pressure gradient
- External force
- Radiation
- Temperature gradient

Answer: Option c

Explanation: Radiation is not one of the driving forces that contribute to mass transfer. Pressure gradient, external force, and temperature gradient are the driving forces that contribute to the mass transfer.

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